Abstract: Turbulence and magnetic fields stand at the crossroads of astrophysical and cosmological inquiry, bridging microscopic physics, such as cosmic rays, to the large-scale galaxy cluster evolution. Despite their paramount importance, a thorough understanding of their characteristics has remained elusive. In this thesis, I explore the properties of magnetohydrodynamic (MHD) turbulence within a partially ionized medium through 3D MHD simulations of two-fluids (ions and neutrals), as well as the influence of stellar feedback. Furthermore, mapping the 3D magnetic field in spatial three dimensions has posed a century-long challenge. In this thesis, based on the anisotropic properties of MHD turbulence, I introduce three innovative techniques for tracing the 3D magnetic field: the Velocity Gradient Technique and the use of Convolutional Neural Networks. I will illustrate how these advancements in 3D magnetic field mapping significantly enhance our comprehension of star formation, Galactic magnetic fields, the CMB foreground polarization, Seyfert activities in nearby galaxies, and the evolution of galaxy clusters.